solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks.

1. [-/1 Points] DETAILS SCALCET9 14.5.003.EP. Consider the following. z = xy's - x2y, x= +2 + 1, y = +2 - 1 Find each of the following. dz dx dz dy dx dt dy dt Use the chain rule to find _ dt Need Help? Read It 2. [-/1 Points] DETAILS SCALCET9 14.5.004. Use the chain rule to find dz dt Z = -y x=e", y=ent x + 5y dz It Need Help? Read It3. [-/1 Points] DETAILS SCALCET9 14.5.005. Use the chain rule to find dz dt z = sin(x) cos(y), x = vt, y => dt Need Help? Read It 4. [-/1 Points] DETAILS SCALCET9 14.5.011. Use the chain rule to find . dz - and Oz at z = (x- y) , x =s't, y= st2 Oz as Oz at Need Help? Read It5. [-/1 Points] DETAILS SCALCET9 14.5.013. Use the chain rule to find oz and at z = In(4x + 5y), x = 5 sin(t), y = t cos(s) dz as Oz at Need Help? Read It 6. [-/1 Points] DETAILS SCALCET9 14.5.018. Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies. U (7, 4) = 2 V(7, 4 ) = 9 U - (7, 4) = -2 VS (7, 4 ) = -4 U. (7 , 4 ) = 3 V. (7 , 4 ) = -9 G (2, 9) = 6 G (2, 9) = -8 Find R (7, 4) and R.(7, 4). R (7 , 4 ) = R. ( 7 , 4 ) = Need Help? Read It7. [-/1 Points] DETAILS SCALCET9 14.5.025.EP. Consider the following. z=x* + xy, x=s+2t - u, y =stu- Find the following partial derivatives. az as az at az du Find oz oz az when s = 5, t = 1, U = 4. ds' at du az as at az au Need Help? Read It8. [-/1 Points] DETAILS SCALCET9 14.5.032. Use the equation OF dy ax dy OF ay to find Jy dx cos(xy) = 3 + sin(y) dy = Need Help? Read It 9. [-/1 Points] DETAILS SCALCET9 14.5.038. Use the equations OF OF oz ax dy and Ox av az az to find _ and az ax 3yz + 4x In(y) = z2 oz ax oz ay Need Help? Read It10. [-/1 Points] DETAILS SCALCET9 14.5.039.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = v 1 + t, y = 8 + t, where x and y are measured in centimeters. The temperature function satisfies Tx(2, 9) = 5 and T, (2, 9) = 9. How fast is the temperature rising on the bug's path after 3 seconds? (Round your answer to two decimal places.) .C/s Need Help? Read it Watch It Master It 11. [-/1 Points] DETAILS SCALCET9 14.5.043. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The length f, width w, and height h of a box change with time. At a certain instant the dimensions are f = 3 m and w = h = 7 m, and f and w are increasing at a rate of 2 m/s while h is decreasing at a rate of 8 m/s. At that instant find the rates at which the following quantities are changing (a) the volume (in m /s) | m'/s (b) the surface area (in m2/s) m 2/ s (c) the length of a diagonal (in m/s) (Round your answer to two decimal places.) m/s Need Help? Read It Watch It